And I have to start off with a non-committal: it depends. What it depends on is the intention for the entire workout.
I always recommend to warm-up prior to lifting weights but a warm-up may not constitute a complete cardiovascular workout which – if you are healthy and can work out in proper heart rate zones – should leave you a a little fatigued even after a short rest. Cardiovascular workouts usually involve the large muscle groups of the legs. This would not be the best scenario it you went to the gym with the plan to work out the lower body to improve limit strength since you are pre-fatigued.
However, if you plan to work out on strength endurance, the problem of pre-fatigued muscles may not present such a dilemma.
If I look at my workout routine while I still worked in the corporate world, I personally always started with 30 minutes of cardio followed by whatever weight training I wanted to do. It was pretty much with the intention of killing two birds with one stone. My time was limited, and – speaking only for myself – my weight training ambitions were rather moderate. So that worked well for me.
So there is no final answer to your question. It has to be viewed in the context of a person’ life and exercise goals.